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Chantal DavidView profile

Professor

• Number Theory
• Elliptic Curves
• L-functions
• +1 more

Chantal David is a Professor in the Department of Mathematics and Statistics at Concordia University. Her research focuses on number theory and its intersections with mathematical statistics. Formal Affiliation: Concordia University, Department of Mathematics and Statistics Email: chantal.david@concordia.ca Office: Library Building, LB 927.09 Research Interests revolve around Number Theory , particularly: L-functions and their non-vanishing properties Elliptic curves over finite fields and function fields Statistics of group structures and root numbers Connections to random matrix theory and metaplectic functions Extremal primes and Frobenius distributions Drinfeld modules and supersingular reductions Article Trends show a focus on cubic and quartic L-functions, non-vanishing phenomena, and statistical properties of elliptic curves over finite fields. Recent work explores metaplectic theta functions, extreme value distributions, and one-level density analysis. Labs & Teams : She is affiliated with the Montreal Number Theory Group (CICMA) .

Eric LarsonView profile

Associate Professor

• Algebraic Geometry
• Brill-Noether Theory
• Moduli Spaces
• +3 more

Eric Larson is an Associate Professor at Brown University's Department of Mathematics, specializing in algebraic geometry. His research focuses on moduli spaces, Brill-Noether theory, and algebraic curves. He collaborates with notable mathematicians such as Isabel Vogt and Izzet Coskun on topics like normal bundles, Chow rings, and stability conditions. Larson actively engages in academic outreach, organizing Putnam competition practices and undergraduate colloquia. He has developed computational tools for studying elliptic curves' Galois representations and contributed to expository works on interpolation problems and LaTeX accessibility.

Brian ConradView profile

Professor

• Number Theory
• Arithmetic Geometry
• Algebraic Geometry
• +3 more

Brian Conrad is a Professor of Mathematics at Stanford University, specializing in number theory and arithmetic geometry. He holds a position in the Department of Mathematics and has contributed extensively to algebraic geometry, algebraic number theory, and representation theory. His research encompasses foundational work on reductive groups, pseudo-reductive groups, and their applications in arithmetic contexts. Dr. Conrad is an editor for the Journal of the AMS, Algebra and Number Theory, and IMRN. He has organized numerous learning seminars, including those on étale cohomology and the BSD conjecture, and has taught advanced courses on algebraic geometry, class field theory, and modular forms. His work bridges classical algebraic geometry with modern arithmetic applications, emphasizing foundational proofs and geometric intuition. His editorial roles and seminar leadership reflect his commitment to advancing mathematical exposition and education. Education details are not explicitly provided in the texts, but his academic trajectory includes significant contributions to the field through publications and mentorship. Dr. Conrad's research has led to advancements in areas such as the classification of algebraic groups, étale cohomology, and the arithmetic of elliptic curves. His collaborative work with mathematicians like Chai, Oort, and Prasad has produced influential monographs, including Pseudo-reductive Groups and Complex Multiplication and Lifting Problems .

Jeremy HahnView profile

Assistant Professor

• Algebraic Topology
• Structured Ring Spectra
• Chromatic Homotopy Theory
• +4 more

Jeremy Hahn is an Assistant Professor at the Massachusetts Institute of Technology (MIT), affiliated with the Department of Mathematics within the School of Science. His research focuses on Algebraic Topology, particularly structured ring spectra, chromatic homotopy theory, and equivariant homotopy theory. Supported by grants from the Sloan Foundation and the National Science Foundation (DMS-1803273), his work has contributed to foundational advances in topological K-theory, algebraic K-theory, and manifold topology. Education details are not explicitly listed, though past teaching roles at Harvard University suggest prior academic training. His research interests span topics including: Structured ring spectra constructions (e.g., truncated Brown-Peterson spectra) Chromatic redshift phenomena and algebraic K-theory Equivariant orientations and C_p actions Applications of homotopy theory to manifold classification Notable recent work includes counterexamples to Ravenel's telescope conjecture, advancements in motivic filtrations of topological cyclic homology, and the construction of multiplicative structures on classical spectra. Collaborations with researchers such as Robert Burklund, Dylan Wilson, and Allen Yuan reflect his active engagement in the global topology research community. Teaching includes advanced courses like Algebraic Topology I (18.905) and past roles as a teaching assistant for Linear Algebra (18.06) and multivariable calculus at MIT. His research has been supported by multiple NSF grants and the Sloan Fellowship, indicating sustained academic excellence and leadership in the field.

Matthew EmertonView profile

Professor

• Number Theory
• Arithmetic Geometry
• Automorphic Forms
• +3 more

Matthew Emerton is a Professor in the Department of Mathematics at the University of Chicago, part of the Physical Sciences Division. He specializes in number theory, arithmetic geometry, and the Langlands program. His research focuses on automorphic forms, Galois representations, and p-adic methods in arithmetic geometry. Education: BSc (Hons) from the University of Melbourne (1993), PhD in Mathematics from Harvard University (1998), advised by Barry Mazur. Research Highlights: Pioneered work on the p-adic Langlands program, moduli stacks of Galois representations, and prismatic cohomology. Authored over 50 publications, including foundational works on p-adic Hodge theory and local-global compatibility. Awards: Alfred P. Sloan Doctoral Dissertation Fellowship (1997-98), Rackham Summer Faculty Fellowship (1999). Grants: Multiple NSF awards (e.g., DMS-2201242 for 'Arithmetic Aspects of the Langlands Program', DMS-1952705 for geometric aspects of the p-adic Langlands program). Students: Mentored 25+ PhD students and postdocs, many contributing to number theory and representation theory.

Urs HartlView profile

Professor

• Arithmetic Geometry
• Algebraic Number Theory
• Representation Theory
• +3 more

Prof. Dr. Urs Hartl is a faculty member in the Department of Mathematics and Computer Science at the University of Münster, affiliated with the Faculty of Mathematics and Computer Science. He is an Investigator in Mathematics Münster and a member of the Collaborative Research Centre (CRC) 1442 'Geometry: Deformations and Rigidity.' His research focuses on arithmetic geometry, representation theory, algebraic number theory, and arithmetic of function fields. He holds a prominent position in the field, contributing to areas such as Shimura varieties, p-adic Hodge theory, and the Langlands program. Affiliations: Member of CRC 1442 Geometry Investigator in Mathematics Münster Research Interests: Arithmetic algebraic geometry Algebraic number theory Arithmetic of function fields Structure theory of Shimura varieties p-adic Hodge theory p-adic Langlands programme Model theory Recent Publications: Hartl's recent work includes studies on moduli stacks of global G-shtukas, periods of Drinfeld modules, and p-adic Galois representations. His research emphasizes foundational contributions to arithmetic geometry and number theory, often involving collaborations with leading mathematicians such as Rajneesh Kumar Singh and Eva Viehmann. Grants & Advising: Hartl’s involvement in CRC 1442 reflects his leadership in geometric research. While specific advising details are not provided, his extensive publications suggest active mentorship in advanced mathematical research. Labs/Teams: Collaborates within the Mathematics Münster research group and the CRC 1442 team, focusing on geometric and arithmetic structures.

Ana CaraianiView profile

Professor

• Number Theory
• Arithmetic Geometry
• Langlands Program
• +3 more

Ana Caraiani is a Royal Society University Research Fellow and Professor in the Department of Mathematics at Imperial College London, specializing in Number Theory and Arithmetic Geometry. She is a member of the Number Theory group, focusing on the Langlands program, Shimura varieties, and p-adic Galois representations. Her work bridges arithmetic geometry and representation theory, with contributions to modularity lifting theorems, cohomology of Shimura varieties, and local-global compatibility in the Langlands program. Education: She earned a Ph.D. in Mathematics from Harvard University in 2012. She held positions as a Veblen Research Instructor (2013–2015) and Veblen Fellow (2015–2016) at the Institute for Advanced Study's School of Mathematics. Research Interests: Her research emphasizes the classical and p-adic Langlands programs, Shimura varieties, arithmetic geometry, and moduli stacks of Galois representations. Specific topics include vanishing theorems for cohomology, modularity of elliptic curves over CM fields, and applications of perfectoid spaces. Key Contributions: Caraiani has advanced the proof of modularity of elliptic curves over imaginary quadratic fields, established vanishing theorems for Shimura varieties with torsion coefficients, and contributed to the potential automorphy of Galois representations over CM fields. Her work links geometric approaches to arithmetic conjectures, such as the Sato-Tate and Ramanujan conjectures. Awards and Recognition: Royal Society University Research Fellowship (202?), Veblen Research Instructor/Fellowships (2013–2016), and contributions to major collaborative projects like the Potential Automorphy over CM Fields paper in the Annals of Mathematics.

David RohrlichView profile

Professor

• Number Theory
• Algebraic Number Theory
• Arithmetic Geometry
• +3 more

David Rohrlich is a Professor of Mathematics and Statistics at Boston University, serving as Director of Graduate Studies. His primary affiliation is with the Department of Mathematics and Statistics. He specializes in Number Theory, focusing on topics such as Artin representations, arithmetic statistics, and Galois theory. His research explores areas including algebraic number theory, arithmetic geometry, and representation theory. Notable contributions include studies on self-dual Artin representations, quaternionic structures in arithmetic statistics, and the interplay between Galois representations and L-functions. Rohrlich has published extensively on topics such as Mordell-Weil groups, average multiplicities, and dihedral Artin representations. His work often involves intricate connections between algebraic structures and number-theoretic phenomena. He holds a PhD and has advised numerous graduate students (though specific names are not listed here). His office is located in CDS 433, with regular in-person and virtual office hours.

Lawrence C. WashingtonView profile

Professor

• Number theory
• Cyclotomic fields
• Elliptic curves
• +5 more

Lawrence C. Washington is a Professor of Mathematics at the University of Maryland, College Park . His office is located in Mathematics Building 1105, and he can be reached at lcw@math.umd.edu . Teaching & Courses: In Spring 2023 he is teaching Cryptography 456 (TuTh 11:00–12:15) and co-organising the Algebra Seminar (MW 2–3). Office hours are held Tuesdays 1:30–2:30 and Thursdays 10:00–10:50. Research Interests: His work centres on number theory , with particular emphasis on cyclotomic fields , elliptic curves , cryptology , and Iwasawa theory . He has made extensive contributions to the study of p-adic L-functions , class groups , heuristics for class numbers , and the arithmetic of elliptic curves, often bridging deep theoretical questions with computational investigations. Textbooks & Scholarly Output: Washington is the author of several widely-used textbooks: Introduction to Cryptography with Coding Theory (3rd ed.) Introduction to Cyclotomic Fields Elliptic Curves: Number Theory and Cryptography An Introduction to Number Theory with Cryptography (2nd ed.) Elementary Number Theory Recent Publication Trends: Over the past five years his papers have focused on heuristics for Iwasawa invariants , anti-cyclotomic extensions , class groups of real cyclotomic fields , and analytic estimates for sums of prime powers . The work is characterised by a synthesis of algebraic, analytic, and computational techniques, frequently yielding explicit examples and numerical data that inform broader conjectures in algebraic number theory. Extracurricular Interests: Outside mathematics, Washington enjoys running and playing the bassoon , and he maintains a light-hearted page devoted to his favourite intersection in Chevy Chase, MD. Advising & Grants: While the provided text does not enumerate individual students or specific grants, his extensive publication record and long-standing professorship indicate ongoing supervision of graduate research and participation in funded projects in number theory and cryptography.

Elena MantovanView profile

Professor

• Arithmetic Geometry
• Number Theory
• Moduli Spaces
• +3 more

Elena Mantovan is the Taussky-Todd-Lonergan Professor of Mathematics at the California Institute of Technology (Caltech), within the Department of Mathematics under the Division of Physics, Mathematics and Astronomy. She holds a Laurea from the University of Padova (1995), an M.A. from Harvard University (1998), and a Ph.D. from Harvard (2002). Her research focuses on Arithmetic Geometry and Number Theory, particularly the study of moduli spaces of abelian varieties, Barsotti-Tate groups, and the arithmetic theory of Shimura varieties. Her work contributes to the Langlands program, exploring connections between automorphic forms and Galois representations. Elena joined Caltech as an Assistant Professor in 2005, advancing to Associate Professor (2010), full Professor (2010-2023), and her current title (2023-). She served as Executive Officer for the Department of Mathematics from 2016 to 2019. Her research interests emphasize Shimura varieties, Newton stratifications, and cohomological studies, reflecting her expertise in algebraic geometry and number theory. Despite no listed awards, her scholarly contributions include foundational work on Rapoport-Zink spaces and Igusa varieties. Elena’s advising and grants are not explicitly detailed in the provided texts, though her role as an academic leader suggests involvement in mentorship and institutional projects. She maintains an office in Sloan Hall and collaborates on initiatives like the Southern California Number Theory Day Conference and the Number Theory seminar.

Dima ArinkinView profile

Professor

• Algebraic Geometry
• Geometric Langlands Program
• Moduli Spaces
• +3 more

Dima Arinkin is a Professor in the Department of Mathematics at the University of Wisconsin–Madison, specializing in algebraic geometry with significant contributions to geometric representation theory and mathematical physics. His research focuses on: Geometric Langlands Program: Developing frameworks connecting automorphic forms and Galois representations through geometric methods Moduli Spaces: Analyzing spaces of algebraic connections, Higgs bundles, and their compactifications D-modules: Studying systems of linear differential equations via algebraic geometry Integrable Systems: Investigating geometric structures in soliton theory and Painlevé equations Irregular Singularities: Exploring connections with irregular behavior on algebraic curves Analysis of his publications (2008-2016) reveals consistent advancement in geometric Langlands through derived algebraic geometry techniques, particularly in relating singular support of sheaves to automorphic forms and establishing oper structures for connections. No scientific awards are documented in the provided materials. No information regarding student advisement or research grants appears in the source texts.

Maxim KontsevichView profile

Professor

• Mathematical Physics
• Algebraic Geometry
• Deformation Quantization
• +5 more

Maxim Kontsevich is a permanent professor at the Institut des Hautes Études Scientifiques (IHÉS), holding the AXA Chair for Mathematics since 1995 and a visiting chair at Rutgers University (one month annually since 1997). Born in 1964 in Khimki, USSR, he earned his PhD from Bonn University in 1992. His career includes visiting positions at Harvard, the Institute for Advanced Study, and Berkeley, where he was a professor from 1993 to 1995. His research spans mathematical physics, algebraic geometry, and non-commutative geometry. Notable contributions include deformation quantization, mirror symmetry, and motivic integration. His work bridges algebraic structures with geometric and physical concepts, influencing areas like topological field theories, string theory, and integrable systems. Awardees of Fields Medal (1998), Crafoord Prize (2008), and Breakthrough Prize (2014), he also holds editorial roles at Compositio Mathematica and Publications Mathématiques IHÉS. His over 50 publications explore advanced topics such as quantum cohomology, Hodge theory, and categorical structures in geometry.

Mark KisinView profile

Professor

• Galois representations
• p-adic Hodge theory
• Shimura varieties

Mark Kisin is the Perkins Professor of Mathematics at Harvard University. His research focuses on Galois representations, p-adic Hodge theory, and Shimura varieties. He has made significant contributions to number theory and algebraic geometry. Research Interests Kisin's work bridges deep questions in number theory with algebraic geometry. His primary areas include Galois representations, p-adic Hodge theory, and Shimura varieties, with applications to modular forms and arithmetic geometry. Recent Publications His recent articles explore topics such as prismatic cohomology, essential dimension, Honda-Tate theory, and Hecke orbits. These works highlight his expertise in Shimura varieties and Galois representations, often involving collaborations with leading mathematicians like B. Farb and J. Wolfson. Editorial Involvement Kisin has served on the editorial boards of prestigious journals including Inventiones (2007–present), Cambridge Journal of Mathematics (2013–present), and Algebra and Number Theory (2013–2015).

Peter SchneiderView profile

Professor

• Arithmetic geometry
• Representation theory
• Cohomology theories
• +7 more

Prof. Dr. Peter Schneider is a faculty member at the University of Münster, affiliated with the Faculty of Mathematics and Computer Science and the Department of Mathematics and Computer Science . He is a principal investigator in the CRC 1442 Geometry: Deformations and Rigidity and contributes to the Mathematics Münster cluster. University: University of Münster School: Faculty of Mathematics and Computer Science Department: Department of Mathematics and Computer Science Academic Rank: Professor His research focuses on arithmetic geometry and representation theory , particularly the p-adic Langlands program , cohomology theories in mixed characteristics, and noncommutative algebraic structures. He investigates derived categories of p-adic representations, moduli spaces of Galois representations, and geometric approaches to automorphic forms. He has supervised numerous students, including Torsten Schoeneberg (2009), Marten Bornmann (2009), and Marius Kley (2016, 2019). His collaborative works with Rachel Ollivier, Otmar Venjakob, and Marie-France Vigneras explore modular Hecke algebras, Iwasawa theory, and (phi, Gamma)-modules. Emails: pschnei@wwu.de pschnei@uni-muenster.de Workshops Organized: Noncommutative Algebras (2006) Instructional workshop on noncommutative main conjectures (2011) International workshop on K-types for p-adic groups (2003)

• Algebraic Number Theory
• Elliptic Curves
• Arithmetic Geometry
• +8 more

Professor Tim Dokchitser is the Heilbronn Chair in Algebraic/Arithmetic Geometry at the School of Mathematics, University of Bristol. His research focuses on algebraic number theory, elliptic curves, arithmetic of L-functions, Galois theory, and computational algebra. He actively explores connections between number theory and finite groups, using computer experiments to advance conjectures like the Birch-Swinnerton-Dyer Conjecture. BSc, Lund University MSc, Lund University PhD, University of Utrecht MA, University of Cambridge His research spans hyperelliptic curves over local fields, Weil representations, tame Galois torsion, and finite group character formulas. Recent work includes computational approaches to Frobenius traces and étale cohomology in hyperelliptic curve quotients. Articles (2023-2025) highlight advancements in arithmetic geometry, zero-knowledge cryptography, and Galois representation theory. Scientific awards include a University Research Fellowship (2011-2014) for elliptic curves and L-functions. He leads projects like the 2015-2018 study on hyperelliptic curves and contributes to collaborations across arithmetic geometry. His computational methods have inspired conjectures in motivic cohomology and modular deformations.